A109581 E.g.f.: x/(1+x-x^3).

0, 1, -2, 6, 0, -120, 1440, -10080, 40320, 362880, -10886400, 159667200, -1437004800, 0, 348713164800, -9153720576000, 146459529216000, -1067062284288000, -25609494822912000, 1338096104497152000, -34060628114472960000, 510909421717094400000

Offset: 0

Author

Roger L. Bagula, Jun 29 2005

Keywords

• sign

Crossrefs

Sequence having -G as o.g.f. is A104769.

Programs

Maple

G:=x/(1+x-x^3): Gser:=series(G,x=0,26): 0,seq(n!*coeff(Gser,x^n),n=1..23); # yields signed sequence

Mathematica

g[x_] = x/(-1 - x + x^3) h[x_, n_] = Dt[g[x], {x, n}] a[x_] = Table[h[x, n], {n, 0, 25}]; b = a[0]
With[{nn=30},CoefficientList[Series[x/(1+x-x^3),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Nov 21 2024 *)

Formula

D-finite with recurrence a(n) + n*a(n-1) - n*(n-1)*(n-2)*a(n-3) = 0. - R. J. Mathar, Aug 20 2021